Zero in division

This is a complete lesson for third grade, with explanations and exercises, about dividing by zero. We study the idea of sharing bananas between zero persons, which is absurd. Even saying that division by zero equals zero doesn't work, because then the check by multiplication fails.

What do you think
6 ÷ 0 would be?

We could think of sharing 6 bananas between 0 persons. But that doesn't make
sense. We can't even talk about how many each
one gets, because there is no one around.

We could think of making groups of 0. How many groups would you get?
Again, you would not get anywhere, you would never get those 6 bananas put
into groups of 0.

You might think that maybe 6 ÷
0 = 0 or that each person gets zero bananas. Check it with multiplication! You
would get 0 × 0 = 6, which
is not true! So 6 ÷
0 = 0 does not work either.

Dividing six by zero (6 ÷ 0) is “undefined.”
Basically, you can't do it.

What about 0 ÷
0? Couldn't we say 0 ÷
0 = 0?

0 ÷ 0 is hard. The
answer could be zero, but actually the answer could be any number :

How to set up algebraic equations to match word problems
Students often have problems setting up an equation for a word problem in algebra. To do that, they need to see the RELATIONSHIP between the different quantities in the problem. This article explains some of those relationships.